Kuhn poker equilibrium with CFR+

What does a real call return?

After 200,000 iterations, the game value is -0.0556, against the analytical −1/18 ≈ -0.0556, with exploitability 0.00029.

Recorded on 2 November 2026 through the public MCP endpoint, service release 0.17.1. Inputs and full responses, response SHA-256 87dd476f9e6c…. Verdict values are the literal values the tool returns. Run the same inputs yourself to compare; elapsed times vary, and a new release may change the figures.

Checked against

• Kuhn poker value −1/18, probability normalization, qualitative equilibrium checks and pure best-response exploitability.

Recorded on release 0.16.1. These checks cover the listed cases, not every input. Evidence cards.

How it works

The solver applies regret-based self-play to two-player Kuhn poker. It reports decision probabilities, game value and exploitability rather than interpreting the behaviour of real players.

Inputs and units

Choose a bounded iteration count. The demonstration uses 200,000 iterations; increasing the count explores convergence for this particular toy game.

What the result contains

A strategy table, estimated game value and exploitability make the computation inspectable. The analytical reference game value is −1/18 for the first player.

Example MCP call

{
  "name": "solve_equilibrium",
  "arguments": {
    "iterations": 200000
  }
}

Send this tool name and arguments through a connected MCP client. Discover the authoritative input schema with tools/list.

Call this engine in one command

Node.js 20+ and npm. This downloads a small remote MCP client; it does not install the engine locally.

npx --yes --package https://scorecompute.com/downloads/scorecompute-call-0.14.2.tgz scorecompute-call solve_equilibrium --arguments '{"iterations":200000}'

Client download, PowerShell input and verification →

Cite this engine

Engine identified by source hash, source SHA-256 d33dd25819b1…. Evidence recorded on release 0.16.1; the public service currently runs 0.17.1. Replace the access date when you cite it.

ScoreCompute. Kuhn poker equilibrium with CFR+ (solve_equilibrium), identified by source hash, source SHA-256 d33dd25819b1219bc1dc869d4ba093a96bd3b49d1b67933ef7bea2716c269511. Evidence release 0.16.1, service release 0.17.1. https://scorecompute.com/engines/solve-equilibrium/ (accessed YYYY-MM-DD).

All engine citations · Evidence card

Execution and availability

ScoreCompute exposes this tool through MCP Streamable HTTP. Rust computation runs on a connected worker; the public website and MCP gateway run separately. Among these 22 scientific tools, CUDA is implemented for simulate_pi; the other scientific engines run on CPU. The separate contributor network runs two compiled public workloads: a π estimate and fixed synthetic schedule probes. Requests are bounded and concurrent work may be refused when capacity is occupied.

Record inputs, assumptions and returned provenance when sharing a result. The public observatory displays software client names and tool activity, without publishing calculation arguments or results.